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3 years ago

Complete the coordinate proof of the theorem.

Mathematics

2 answers:

Flauer [41]3 years ago

8 0

Answer:

Step-by-step explanation:

THESE ARE THE CORRECT ANSWERS

mojhsa [17]3 years ago

3 0

C(a,b), because the x-coordinate( first coordinate) is a (seeing as it is situated directly above point B, which also has an x-coordinate of a) and the y-coordinate ( second coordinate) is b (seeing as it is situated on the same horizontal level as point D, which also has a y-coordinate of b)

the length of AC can be calculated with the theorem of Pythagoras:

length AB = a - 0 = a
length BC = b - 0 = b

seeing as the length of AC is the longest, it can be calculated by the following formula:

It is called "Pythagoras' Theorem" and can be written in one short equation:

a^2 + b^2 = c^2 (^ means to the power of by the way)

in this case, A and B are lengths AB and BC, so lenght AC can be calculated as the following:

a^2 + b^2 = (length AC)^2
length AC = √(a^2 + b^2)

Extra information: Seeing as the shape of the drawn lines is a rectangle, lines AC and BD have to be the same length, so BD is also √(a^2 + b^2). But that is also stated in the assignment!

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In the calm waters of an inlet, Manon's boat moves with a velocity (speed and direction) vector \vec{b_1} = (3,4) b 1 =(3,4)

andrew-mc [135]

Answer with Step-by-step explanation:

We are given that

$b_1=(3,4)$

$b_2=(1,1)$

We have to find the speed of river's current and the direction of current flowing.

$b=b_2-b_1=(1,1)-(3,4)=(-2,-3)$

Speed of river's current= $\mid b\mid$

Speed of river's current= $\sqrt{(-2)^2+(-3)^2}$

Speed of river's current= $\sqrt{13} m/s$

By using the formula

$\mid r\mid =\sqrt{x^2+y^2}$

Direction of current flowing, $\theta=tan^{-1}(\frac{y}{x})$

$\theta=tan^{-1}(\frac{-3}{-2})=56.3^{\circ}$

The angle lies in third quadrant therefore

$\theta=180+56.3=236.3^{\circ}$

3 0

2 years ago

Rob is making a tent out of canvas in the shape of a square pyramid. Each side of the square base is 6 feet long, and the height

Elena L [17]

The amount of balloons in the tent is 125.075 feet cube. From the given options, approximately, option D is correct

Solution:

Given, Rob is making a tent out of canvas in the shape of a square pyramid. Each side of the square base is 6 feet long, and the height is 6.3 feet.

Rob filled the tent with balloons,

We have to find which measurement BEST describes the amount of balloons in the tent?

As tent if filled with balloons the amount of balloons equals with volume of tent.

Volume of tent is given as:

$\text { volume of tent }=a^{2}+2 a \sqrt{\frac{a^{2}}{4}+h^{2}}$

where "a" is side length and "h" is height.

$\begin{array}{l}{\text { Then, Volume }=6.3^{2}+2(6.3) \sqrt{\frac{6.3^{2}}{4}+6^{2}}} \\\\ {=39.69+12.6 \sqrt{9.925+36}} \\\\ {=39.69+12.6 \times 6.7766=39.69+85.385} \\\\ {=125.075 \mathrm{ft}^{3}}\end{array}$

Hence, from the given options, approximately, option D is correct.

6 0

2 years ago

Read 2 more answers

What is the equation of the line that passes through the point (6,14) and is parallel to the line with the following equation? y

Gekata [30.6K]

Answer:

$y=\displaystyle-\frac{4}{3}x+22$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept
Parallel lines always have the same slope (m)

Determine the slope (m):

$y=\displaystyle-\frac{4}{3}x -1$

The slope of the given line is $\displaystyle-\frac{4}{3}$ , since it is in the place of m in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be $\displaystyle-\frac{4}{3}$ . Plug this into y=mx+b: